Measurement of Length Parallax Method

Description:

Indirect Method

When we cannot reach both the ends of length, the measurement is done by indirect method. The use of indirect method is again classified depending upon the distance −

• Large distance
• Small distance

Large distance

For measurement of length of large distance we use the following indirect methods −

We calculate the length using a formula −

length = velocity × time

Trigonometry / parallax method

Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a metre scale. An important method in such cases is the parallax method.

To calculate large distance, the parallax method uses two observation points for the single object as shown in figure.

Equation used to calculate the distance is given by −

r = x/θ

Where,

r = Distance to be measured.

x = Distance between observation points

θ = Parallax angle.

Steps to implement parallax method

Suppose we need to calculate the distance of a middle range star from earth.

Step 1 − The two observation points are decided depending upon the location of the earth. The star is observed with a difference of 6months in between the two observation points.

Step 2 − To measure the distance, the formula of parallax method is used −

r = x/θ

Where,

r = Distance to be measured.

x = Distance between observation points

θ = Parallax angle.

Here, the distance between the observation points is known i.e.

x = 2 aU

Calculating the parallax angel is a difficult task, so as to make it easy, the concept of “rays coming from a faraway star is always parallel” is used.

Step 3 − A faraway star is observed together with the middle range star from both the observation points, so as to calculate the parallax angle. From figure −

θ = θ₁ + θ ₂

Step 4 − As both ‘the distance between observation points’ and ‘parallax angle’ is known, the distance between earth and middle range star can be measured easily by −

r = x/θ

∴ r = 2 aU/θ₁ + θ₂